What you need to do is some research. Find a reputable artist, experienced with coverups and see what they can do. Get multiple recommendations from people with good work.
Did you not look at what they were going to tattoo on you before they started????
Take a closer look at his work. IMHO there is very little black/grey contrast, it's very monotone, and some of it is so dense it's hard to read. I think that is what would happen to your drawing if this guy does it. You need some negative space to provide contrast, otherwise it will look like a big blob of ink from 10 feet away.